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MonomialList may provide functionality you're looking for here. P[x,y,z]=x y^2 z + 2x y z^2 + x^2 y^2; Q[x,y,z]=x^2 y z - x y z^2 + x^2 z^2; P[x,y,z]+a Q[x,y,z]//Expand will yield x^2 y^2 + a x^2 y z + x y^2 z + a x^2 z^2 + 2 x y z^2 - a x y z^2 Now, to get the factorization you're looking for, MonomialList[x^2 y^2 + a x^2 y z + x y^2 z + a x^2 z^2 + ...



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